How to change the Viewpoint Shading like in older Blender versions
You seems to be correct - with Flat type Lightning you can use Texture or Vertex Paint only, if you want use Workbench.
I wanted to use Material type, but it reflects only Viewport Display setup (single RGB Color).
So the only one way I see is use Eevee material.
Plug Vertex Color node and Image texture node into Mix RGB node, than directly into Output without any shader.
To see colours untouched you should change Color Management &gt; Standard.